Envelope solitary waves and their reflection and transmission due to impurities in a granular material<xref rid="cpb_27_1_014501fn1" ref-type="fn">*</xref> <fn id="cpb_27_1_014501fn1"> <label>*</label> <p>Project supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDA01020304) and the National Natural Science Foundation of China (Grant Nos. 91026005, 11547304, 11275156, 11047010, and 61162017).</p> </fn>

Envelope solitary waves and their reflection and transmission due to impurities in a granular material* *

Project supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDA01020304) and the National Natural Science Foundation of China (Grant Nos. 91026005, 11547304, 11275156, 11047010, and 61162017).

Du Wen-Qing¹, Sun Jian-An¹, Yang Yang-Yang², Duan Wen-Shan^{1, †}

(color online) Comparison between the analytical results of Eq. (4) and the numerical ones of the envelope solitary wave. The dependence of amplitude, group velocity, and the width of the envelope solitary wave on the parameter k are shown in (a₁), (b₁), and (c₁), respectively, where ε = 0.01 and 0.05 ≤ k ≤ 0.95. The dependence of amplitude, group velocity, and the width of the envelope solitary wave on the parameter ε are shown in (a₂), (b₂), and (c₂), respectively, where k = 0.1 and 0.05 ≤ ε ≤ 0.6.